Well, I finally found a proper solution to convert my h.264 TS files, But I'm now suffering another glitch.
After the conversion job the output file has missing frames. Around 20 or 40 seconds of the clip 3 or 4 frames are basically skipped. Apart from that the file is fine.
I have no clue why it happens.
This my basic script:

EDIT: I just checked it again with my original script (not the one with the demuxed files) and it seems to work now as it should. I will do some more tests and give you a feedback. But it looks pretty good right now...